The aim of this work is to look for rescue trajectories that leave the surface of the Moon, belonging to the hyperbolic manifolds associated with the central manifold of the Lagrangian points L1 and L2 of the Earth–Moon system. The model used for the Earth–Moon system
is the Circular Restricted Three-Body Problem. We consider as nominal arrival orbits halo orbits and square Lissajous orbits around L1 and L2 and we show, for a given Dv, the regions of the Moon’s surface from which we can reach them. The key point of this work is the
geometry of the hyperbolic manifolds associated with libration point orbits. Both periodic/ quasi-periodic orbits and their corresponding stable invariant manifold are approximated by means of the Lindstedt–Poincaré semi-analytical approach.